3 citations · 8 across the 12 of their papers we have counts for
17 papers
Quaternionic analogues of Bers's theorem and Iss'sa's theorem
Dong Quan Ngoc Nguyen
In their recent work, Gentili and Struppa proposed a different quaternionic analogue of the notion of holomorphic functions in the complex plane, called \textit{slice regular funct…
A local geometry of hyperedges in hypergraphs, and its applications to social networks
Dong Quan Ngoc Nguyen, Lin Xing
In many real world datasets arising from social networks, there are hidden higher order relations among data points which cannot be captured using graph modeling. It is natural to…
Community detection, pattern recognition, and hypergraph-based learning: approaches using metric geometry and persistent homology
Dong Quan Ngoc Nguyen, Lin Xing, Lizhen Lin
Hypergraph data appear and are hidden in many places in the modern age. They are data structure that can be used to model many real data examples since their structures contain inf…
Weight Prediction for Variants of Weighted Directed Networks
Dong Quan Ngoc Nguyen, Lin Xing, Lizhen Lin
A weighted directed network (WDN) is a directed graph in which each edge is associated to a unique value called weight. These networks are very suitable for modeling real-world soc…
On the generating polynomials for the distribution of generalized binomial coefficients in discrete valuation domains
Dong Quan Ngoc Nguyen
For a discrete valuation domain with maximal ideal such that the residue field is finite, there exists a sequence of polynomials $(F_n(x))_{n \g…
Effectively bounded idempotent generation of certain singular matrices by idempotent matrices over real quadratic number rings
Dong Quan Ngoc Nguyen
Let be a real quadratic number field, where is a positive square-free integer. Let be the ring of integers of . In this paper, we pr…
Polynomial Parametrization for over Quadratic Number Rings
Michael Larsen, Dong Quan Ngoc Nguyen
If is the ring of integers of a number field, then there exists a polynomial parametrization of the set , i.e., an element $A \in \text{SL}_2(\mathbb{Z}[x_1,\ld…
Waring's problem for unipotent algebraic groups
Michael Larsen, Dong Quan Ngoc Nguyen
In this paper, we formulate an analogue of Waring's problem for an algebraic group . At the field level we consider a morphism of varieties and ask w…
The distribution of the Carlitz binomial coefficients modulo a prime
Dong Quan Ngoc Nguyen
For a nonnegative integer , and a prime in , we prove a result that provides a method for computing the number of integers with for wh…
Representation of units in cyclotomic function fields
Dong Quan Ngoc Nguyen
Hilbert's Satz 90 tells us that for a given cyclic extension , a unit of norm in can be written as a quotient of conjugate elements in . For the extensions $\mathbb…
Certain sets over function fields are polynomial families
Dong Quan Ngoc Nguyen
In 1938, Skolem conjectured that is not a polynomial family for any . Carter and Keller disproved Skolem's conjecture for all by prov…
Function field analogues of Bang-Zsigmondy's theorem and Feit's theorem
Dong Quan Ngoc Nguyen
In the number field context, Bang-Zsigmondy's theorem states that for any integers , there exists a prime divisor of such that does not divide …
Algebraic families of hyperelliptic curves violating the Hasse principle
Dong Quan Ngoc Nguyen
In , Colliot-Thélène and Poonen showed how to construct algebraic families of genus one curves violating the Hasse principle. Poonen explicitly constructed an algebraic famil…
Carlitz module analogues of Mersenne primes, Wieferich primes, and certain prime elements in cyclotomic function fields
Dong Quan Ngoc Nguyen
In this paper, we introduce a Carlitz module analogue of Mersenne primes, and prove Carlitz module analogues of several classical results concerning Mersenne primes. In contrast to…
A Carlitz module analogue of the Grunwald--Wang theorem
Dong Quan Ngoc Nguyen
The classical Grunwald--Wang theorem is an example of a local--global (or Hasse) principle stating that except in some special cases which are precisely determined, an element …
The classical umbral calculus, and the flow of a Drinfeld module
Dong Quan Ngoc Nguyen
David Goss developed a very general Fourier transform in additive harmonic analysis in the function field setting. In order to introduce the Fourier transform for continuous charac…
Generalized Mordell curves, generalized Fermat curves, and the Hasse principle
Dong Quan Ngoc Nguyen
A generalized Mordell curve of degree over $\bQ$ is the smooth projective model of the affine curve of the form , where are nonzero integers. A…